Now, in an open or flat Friedmann-Robertson-Walker cosmological model with no cosmological constant, whilst the past 'Big-Bang' singularity corresponds to a spacelike hypersurface in the boundary of the conformal compactification, the future timelike infinity corresponds to a single point.

Given an initial condition on a time-like hypersurface as a mathematical model for the universe, we can determine in which direction a dynamics (supposed here to be deterministic, whether applied to a quantum or to a classical state) causes the entropy to increase or to decrease.